Redline produces decent rear diff oils, both for open and lsd diffs. Can't remember the price though but it's not expensive. You'll need about 1.5l for 3 series.
You can opt to go for ori BMW rear diff oil but I don't know the price for open diff one. BMW does have special LSD oil for their LSD rear diff but it's very expensive. Comes in 500ml bottles @ RM144 each.
I intend to use Royal Purple MAxgear, 75W90, about Rm70/quart. this can be used in manual gearboxes too, example my old iswara manual.
Redline 75W90 is about Rm60/quart.
Is it an open rear diff or Limited Slip Differential (LSD)?
If it's an open diff, most gear oils are fine. Just get a 4 liter bottle of castrol gear oil and it will be just fine. My E34 has been running on that for 4 years without any problems.
If it's a LSD unit, then you would have to use one that is formulated with additional anti friction modifiers. Red Line is pretty good, heard TORCO is even better and as Loafer mentioned, BMW also has its own LSD oil and it's freaking expensive!
On the little aluminium plate that indicates your differential ratio, say 3.25 or 3.64, if there is a 'S' prior to the number, that indicates its a LSD unit.
The other way is to turn one of the wheel and see how the other wheel reacts, if it turn in the same direction, then that also means it's a LSD unit.
i think mine hasn't been changed for 16 years...the original axle oil is supposed to be a high quality oil? i'll check with mechanic again later =) thanks
There's also the alphabet S stamped on the rear diff. You might need to remove all the dust and whatnot that's baked into the rear diff to see it. The easiest way is the aluminum plating which states the ratio as mentioned by albundy.